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Topics in Nevanlinna Theory

  • Editors
  • Serge¬†Lang
  • William¬†Cherry

Part of the Lecture Notes in Mathematics book series (LNM, volume 1433)

Table of contents

  1. Front Matter
    Pages I-2
  2. Serge Lang
    Pages 9-55
  3. Back Matter
    Pages 169-174

About this book

Introduction

These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidimensional holomorphic maps using as domain space finite coverings of C resp. Cn. Conjecturally best possible error terms are obtained following a method of Ahlfors and Wong. This is especially significant when obtaining uniformity for the error term w.r.t. coverings, since the analytic yields case a strong version of Vojta's conjectures in the number-theoretic case involving the theory of heights. The counting function for the ramified locus in the analytic case is the analogue of the normalized logarithmetic discriminant in the number-theoretic case, and is seen to occur with the expected coefficient 1. The error terms are given involving an approximating function (type function) similar to the probabilistic type function of Khitchine in number theory. The leisurely exposition allows readers with no background in Nevanlinna Theory to approach some of the basic remaining problems around the error term. It may be used as a continuation of a graduate course in complex analysis, also leading into complex differential geometry.

Keywords

Complex analysis Meromorphic function Nevanlinna theory differential geometry logarithm number theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093846
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-52785-5
  • Online ISBN 978-3-540-47146-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site